SSC CGL 2024 Tier-I · 18 September 2024, Shift 1 · Quantitative Aptitude · Question 14 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

The sum of five consecutive numbers is 80. Find the largest number.

(a)18
(b)19
(c)15
(d)14

Answer

Why

Correct — A. Five consecutive numbers are symmetric about the middle one, so the middle number is their average.

middle = 80 ÷ 5 = 16

The run is 14, 15, 16, 17, 18.

largest = 16 + 2 = 18 → option (a)

Check: 14 + 15 + 16 + 17 + 18 = 80.

Why the others are wrong

(b)
19 — 19 tops the run 15, 16, 17, 18, 19, which sums to 85. That overshoots the given 80 by 5.
(c)
15 — 15 is the second number in the run, not the last. The question asks for the largest, and the run ends at 18.
(d)
14 — 14 is the smallest of the five. It is the first term, which is what you report if you solve 5n + 10 = 80 for n and stop there.

Concept

For an odd count of consecutive numbers the middle term equals the average, so sum ÷ count lands straight on it.

Five terms: sum ÷ 5 = middle. Three terms: sum ÷ 3 = middle. Seven terms: sum ÷ 7 = middle.

For an even count there is no middle term. The average falls between the two central values, comes out as a half-integer, and you step outward from there.

Writing the run as n−2, n−1, n, n+1, n+2 makes the sum 5n and removes the algebra entirely. Writing it as n, n+1, n+2, n+3, n+4 works too, but then the answer is n + 4, not n.

Key facts

Five consecutive numbers written n−2 to n+2 have sum 5n.
80 ÷ 5 = 16 is the middle number, so the run is 14 to 18.
For an even count of consecutive numbers the average lies between two terms and is not itself a term.

Study next

Consecutive even and odd runs, where the common difference is 2Writing an unknown run as n−2 … n+2 to kill the algebraSum of an arithmetic progression read as count × average

Common traps

Solving 5n + 10 = 80 with n as the first term and then reporting n instead of n + 4
Answering 16, the middle number, because it is what the division gives
Reading 'numbers' as 'even numbers' and stepping by 2

SSC keeps the arithmetic trivial here and moves the difficulty into which term is asked for — smallest, largest or middle.

A two-term even-number version is asked at 26 Sep 2024, 12:30, Quant Q.17.

Related PYQs

No directly related past PYQ was found.